$g(t) = -2t$ $h(t) = -3t^{2}+7t-4(g(t))$ $f(t) = 2t-6-4(g(t))$ $ g(f(-5)) = {?} $
Explanation: First, let's solve for the value of the inner function, $f(-5)$ . Then we'll know what to plug into the outer function. $f(-5) = (2)(-5)-6-4(g(-5))$ To solve for the value of $f$ , we need to solve for the value of $g(-5)$ $g(-5) = (-2)(-5)$ $g(-5) = 10$ That means $f(-5) = (2)(-5)-6+(-4)(10)$ $f(-5) = -56$ Now we know that $f(-5) = -56$ . Let's solve for $g(f(-5))$ , which is $g(-56)$ $g(-56) = (-2)(-56)$ $g(-56) = 112$